Planar isolated and stable fixed points have index =1

DOI10.1016/j.jde.2003.11.002zbMath1052.37011OpenAlexW2026558038MaRDI QIDQ1883115

Francisco Romero Ruiz del Portal

Publication date: 1 October 2004

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2003.11.002

zbMATH Keywords

stabilityflowsfixed-point indexisolated periodic orbitsprime ends compactification

Mathematics Subject Classification ID

Stability of topological dynamical systems (37B25) Fixed-point and coincidence theorems (topological aspects) (54H25) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Fixed points and coincidences in algebraic topology (55M20) Index theory for dynamical systems, Morse-Conley indices (37B30)

Related Items (6)

Isolating blocks of isolated invariant continua and fixed point index ⋮ Translation Arcs and Stability in Two Dimensions ⋮ Indices of the iterates of \(\mathbb R^3\)-homeomorphisms at Lyapunov stable fixed points ⋮ Periodic points of the planar area preserving Poincaré map inside isolating segment ⋮ A Poincaré formula for the fixed point indices of the iterates of arbitrary planar homeomorphisms ⋮ Realization of all Dold's congruences with stability

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